Abstract

This paper proposes a two-dimensional car-following model to tackle traffic flow problems where considering continuum lateral distances enables a simpler or more natural mathematical formulation compared to traditional car-following models. These problems include (i) the effects of lateral friction often observed in HOV lanes and diverge bottlenecks, (ii) the relaxation phenomenon at merge bottlenecks, (iii) the occurrence of accidents due to lane changing, and (iv) traffic models for autonomous vehicles (AVs). We conjecture that traditional car-following models, where the lateral dimension is discretized into lanes, struggle with these problems and one has to resort to ad-hoc rules conceived to directly achieve the desired effect, and that are difficult to validate.